The wave elevation \(\eta (t)\)  is usually specified from a wave spectral process, which resides in a high-dimensional input space. A typical procedure to reduce the dimension is to describe \(\eta (t)\)  by an ensemble of wave groups embedded in its envelope process [1]}, [2]} (see figure REF (a) for an illustration, which is only strictly valid in narrow-band wave spectrum). Specifically, we compute the envelope process \(\rho (t)\)  from \(\eta (t)\)  through the Hilbert transform [3]}, and then construct two-parameter Gaussian-like wave groups \(\rho _c(x)\)  which best fits \(\rho (t)\) :
\(\rho _c(t)\sim A \exp \frac{-(t-t_c)^2}{2L^2},\) 
